I'm back in the Shire, and in the town of Michael Delving. The postman - my mortal enemy - is asking me to deliver the mail.
The mail sits there, with nobody in a hurry to make it go anywhere. Then a package is handed to you, and suddenly the clock is running. If time runs out, the package vanishes and you fail.
You run faster (20%, I think) when carrying mail, which means that you can use the postal service as a sort of ersatz transport system. As long as you never actually finish any of the deliveries you'll have a speed-boosting package available in every town. Just take the package and head off to your destination. Drop the quest when you get to wherever you're going. Given the distances you need to hike in the Shire, this is actually a really attractive option.
But! Before you grab that satchel and run off, you need to be aware that if you get too close to a "Nosy Hobbit" then the package will vanish and you'll fail the quest. Your package vanishes and you have to go back for another one. Their chat indicates that they're trying to stop you for a bit of gossip, although I would really question the prowess of their gossip vs. my knife and my will to complete this quest.
Let's assume that the postman managed to explain all of this to Lulzy without her head exploding. We now rejoin her trip to Michael Delving.
I breeze along the path, the satchel waving in the air behind me. I've never felt so... fast. In just a minute or so I've covered the entire distance to Michael Delving. This whole mail delivery business is strangely liberating. But... do I really care if the mail gets where it's going? I don't really. Now that I'm in town I don't want to bother tracking down the postman. Actually delivering mail pays 90 coppers, but I just don't need money that badly. I've got over fifty silver, which is more money than I've ever had in my life. Besides, if I delivered all the mail then there wouldn't be any left for me to throw away.
I toss the satchel into the bushes and hunt for the mayor.
Glancing back at the bushes, I suddenly realize I've figured out what's been wrong with the post office all this time.
This must be why nobody ever gets their mail. Carriers are likely just random people who take mail because they're in a hurry, and then throw it into the nearest ditch because, hey... it's not my mail, right? This explains so much.
Ah well. As long as I don't need to send any letters I should be fine.